The fundamental building blocks of matter consist of infinitesimal particles from two categories: quarks and leptons. Quarks are bound up into hadrons, such as protons and neutrons. Leptons include the familiar electron, but also its heavier cousin, the muon, which can carry either a positive or negative electric charge (m⁺ or m^-). Muons are produced in the atmosphere in cosmic-ray induced air showers, and because they are quite penetrating they can reach the ground, enter the laboratory through the walls or roof of the building, and be detected with a suitable apparatus. They were first detected and investigated by Bruno Rossi and others in the 1930s and 40s, in the study of air showers. Unlike electrons, muons are unstable and eventually decay into an electron (or positron) and some neutrinos. It is this decay that will be studied in this experiment, and the lifetime of the muon will be measured.

Equipment

• 55-gallon drum of liquid scintillator (a clear mineral-oil based mixture containing 10% by volume of pseudocumene, and small amounts of PPO and Bis-MSB waveshifters)

• Hamamatsu R5912 8"-diameter hemispherical photomultiplier tube (PMT)

• EG&G Ortec Model 871 Timer and Counter

• EG&G Ortec Model 584 Constant Fraction Discriminator

• EG&G Ortec Model 566 Time-to-Amplitude Converter

• EG&G Ortec Model 4002D NIM bin

• Bertan high voltage power supply

• BNC signal cables, including a long delay cable

• Oscilloscope

• OxfordWIN multichannel analyzer (MCA) card and software, Systemax personal computer

• Two small scintillator paddles attached to a vertical metal frame

Consult the literature to learn about muons and particle physics, and the technique of scintillation counting. The MIT "Speed and Mean Life of Cosmic-Ray Muons'' lab manual, available at:

http://web.mit.edu/8.13/www/JLExperiments/JLExp14.pdf  (or click here for a local copy)

can provide some valuable information. Note that this refers to a setup different to what we have here, so the MIT guide should be considered purely indicative.

Familiarize yourselves with the equipment and the various functions of the electronics modules and the MCA. Consult the instrument manuals. Be careful not to operate the PMT beyond the maximum allowable voltage of +1800 V (+2000V for the small paddles). Note that the PMT voltage dividers are rigged for positive HV operation. WARNINGS: beware of shock hazards with the HV power supply (do not operate the supply unconnected); the scintillator is a moderately flammable and toxic substance (do not attempt to open the drum).

With the available components:

1.    Measure the speed of cosmic ray muons and verify that there is an upper limit to velocities, as specified by the special theory of relativity. Do this by accumulating distributions of time differences between signals from the two small scintillator paddles, for different separations between the paddles.

2.    Devise a circuit to measure the lifetime of the muon. Basically, when a muon decays inside the volume of the drum, two pulses of light are produced, due first to the muon itself, and then to the electron (or positron) resulting from the decay. You need to measure the distribution of time differences between the two pulses. How can you extract the muon lifetime from such a distribution? Can you find structure in the distribution that can be attributed to different disappearance modes for the m⁺ and the m^- ? Explain.

Operational hints

Carefully look at all signals on an oscilloscope, externally terminated into 50 ohms. Make sure you understand the PMT output signals, the outputs of all modules in the circuit and the relationship in time of all signals.

Determine the optimal high voltage (HV) at which to operate the PMTs (this will be significantly LESS than the maximum of +1800 V (or + 2000 V)). You could do this by measuring, using the Timer and Counter module, the count rate of pulses as a function of high voltage. You want the HV to be high enough to produce a good-size signal for real muon events, but small enough so as not to generate spurious signals due to other causes (like electronic noise, electrons ejected thermionically from the PMT photocathode material, etc.). For the PMT in the scintillator drum, there should be a nice, clear plateau in the distribution, and the PMT should be operated somewhere on the plateau. For the small paddles, a reasonable HV can be guessed at, then both paddles can be carefully placed on top of each other and signals from both observed simultaneously on the oscilloscope (in the two channels); when a real muon comes through both paddles, simultaneous pulses will be produced, and an idea of the size of muon signals can be had.

When the size of muon pulses has been determined, the threshold voltage to be used in the Constant Fraction Discriminator modules can be determined. Ideally this would cut out much of the noise due to small pulses from other causes, without deteriorating the muon efficiency much.

The MIT write-up refers to the use of a coincidence module. This is not needed here (why?).

In the first part of the experiment, measuring the speed of the muons, you may find it advantageous to measure the time difference for several paddle separations, and to plot the separation as a function of time; the slope is then the speed of the muons. This avoids any possible shifts due to the timing module. Also, since the muons are relativistic and their crossing time short (difficult to measure accurately), it may be a good idea to artificially lengthen the travel time by a constant amount by introducing an appropriate long delay cable somewhere in the circuit.

In the second part of the experiment, measuring the lifetime of the muons, remember that only one PMT produces both pulses (separated in time by several microseconds). One has to be careful not to start and stop the clock module simultaneously with the very first pulse. This can be accomplished again with the judicious use of a long delay cable somewhere in the circuit. What is the effect, if any, of the use of such a long delay cable on the measured muon lifetime?

The observed distribution of time differences in the lifetime measurement should fall exponentially first, then level off to some constant value. What is the physical cause of events in the flat background on top of which rides the exponential from decaying muons?

References

1. A.C. Melissinos, Experiments in Modern Physics, Academic Press, New York (1966).

2. B. Rossi, Cosmic Rays, McGraw-Hill, London (1964).

3. M. W. Friedlander, Cosmic Rays, Harvard University Press, Cambridge (1989).

4. T. K. Gaisser, Cosmic Rays and Particle Physics, Cambridge University Press, Cambridge (1990).

5. W. R. Leo, Techniques for Nuclear and Particle Physics Experiments, 2^nd ed., Springer-Verlag, New York (1992).

6. K. Kleinknecht, Detectors for Particle Radiation, Cambridge University Press, Cambridge (1986).